LICEcap

LICEcap can capture an area of your desktop and save it directly to .GIF (for viewing in web browsers, etc) or .LCF (see below).

LICEcap is an intuitive but flexible application (for Windows and now OSX), that is designed to be lightweight and function with high performance.

LICEcap is GPL free software, each download package includes the source.

Features and options:

Record directly to .GIF or .LCF.
Move the screen capture frame while recording.
Pause and restart recording, with optional inserted text messages.
Global hotkey (shift+space) to toggle pausing while recording
Adjustable maximum recording framerate, to allow throttling CPU usage.
Basic title frame, with or without text.
Record mouse button presses.
Display elapsed time in the recording.
Requirements:

For Windows: Windows XP/Vista/7/8/8.1/10 (might work with reduced functionality on older versions)
For OSX: OS 10.4+ (10.6+ for full feature support), PPC or Intel
A reasonably fast CPU
A healthy amount of RAM (1GB+, especially when encoding to LCF)